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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "FFT with Python"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you want to know how the FFT Algorithm works, Jake Vanderplas explained it extremely well in his blog: http://jakevdp.github.io/blog/2013/08/28/understanding-the-fft/"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is, how it is applied and how the axis are scaled to real physical values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import csv\n",
      "import pandas as pd\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 80
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline --no-import-all"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "First: A synthetic Signal, a simple Sine Wave"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = np.linspace(0, 2*np.pi, 1000, endpoint=True)\n",
      "f = 3.0 # Frequency in Hz\n",
      "A = 100.0 # Amplitude in Unit\n",
      "s = A * np.sin(2*np.pi*f*t) # Signal"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 82
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(t,s)\n",
      "plt.xlabel('Time ($s$)')\n",
      "plt.ylabel('Amplitude ($Unit$)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 83,
       "text": [
        "<matplotlib.text.Text at 0x10fd4dbd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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yij3AWYU6vrj9JbwfAKpDRvzGrbtR7AGWiPhnXw3wFQL++X0o9ABnCvp3PL8H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\n/wErWRpk12kqcQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10fc75dd0>"
       ]
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Do the Discrete Fourier Transform with the Blazing Fast FFT Algorithm"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Y = np.fft.fft(s)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 84
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That's it."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Let's take a look at the result"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(Y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 85,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10ff3f7d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sFMxBI18WLCbDJ1EBISIaHNtcHiBPYZG6J9wDs1AwB410WbDN5QnyFBAiokFx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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10fb289d0>"
       ]
      }
     ],
     "prompt_number": 85
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Hm, looks strange. Something, which is mirrored at the half, right?!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = len(Y)/2+1\n",
      "Y[N-4:N+3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 86,
       "text": [
        "array([ 35.82784530 -3.47926591e-01j,  35.82789273 -2.31947205e-01j,\n",
        "        35.82792118 -1.15972446e-01j,  35.82793066 +2.45137244e-13j,\n",
        "        35.82792118 +1.15972446e-01j,  35.82789273 +2.31947205e-01j,\n",
        "        35.82784530 +3.47926591e-01j])"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Can you see it?\n",
      "\n",
      "And it is something with imaginary parts (the $j$) in it. So let's just take the real part of it with the `abs` command."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(np.abs(Y))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 87,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10f78b210>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wTvqNKRZlYSgLQ1nYQ2UhIiIxqSwSjL73xlAWhrIwlIU9VBYiIhKTyiLBaB5rKAtDWRjK\nwh4qCxERiUllkWA0jzWUhaEsDGVhD5WFiIjEpLJIMJrHGsrCUBaGsrCHykJERGJSWSQYzWMNZWEo\nC0NZ2ENlISIiMaksEozmsYayMJSFoSzsobIQEZGYVBYJRvNYQ1kYysJwbBY2/9VEKgsREYlJZZFg\nNI81lIWhLAzHZnH1r7C2i8pCRERiUlkkGMfOY69DWRjKwlAW9lBZiIhITCqLBOPYeex1KAtDWRjK\nwh4qCxERiUllkWA0jzWUhaEsDGVhD5WFiMhEoA/lyWCaxxrKwlAWhrKwh8pCRERiUlkkGM1jDWVh\nKAtDWdhDZSEiIjGpLBKM5rGGsjCUhaEs7KGyEBGZCPRFgjKY5rGGsjCUhaEs7DFBysLeRhURcboJ\nUhb2fhhlPNE81lAWhrIwHJuFPpQnIiLxprJIMJrHGsrCUBaGsrDHiGXR1NTEo48+yuzZs5kzZw6/\n/vWvAYhEIgSDQXJycliwYAHt7e3R25SVleHz+cjNzWX//v3R/cePHycQCODz+diwYUN0f2dnJ8uW\nLcPn85Gfn8/p06dH+zmKiMifaMSycLvd/NM//ROffPIJH3zwAa+99hqffvop5eXlBINBTp48SUFB\nAeXl5QA0NDSwfft2GhoaqKmpYe3atVhX52hr1qyhsrKSUChEKBSipqYGgMrKStLS0giFQmzcuJFN\nmzbZ/JQTm2PnsdehLAxlYSgLe4xYFunp6dx3330A3HHHHdxzzz2Ew2H27NlDaWkpAKWlpezatQuA\n3bt3U1JSgtvtJisri+zsbOrq6mhtbeXixYvk5eUBsHLlyuhtBt/X0qVLqa2tteeZiojIt5Z8o1c8\ndeoUH330EQ899BBtbW14PB4APB4PbW1tALS0tJCfnx+9jdfrJRwO43a78Xq90f0ZGRmEw2EAwuEw\nM2bM6F9McjJTpkwhEomQmpo65PHXrVtHZmYmACkpKQQCARZdvezdT07TdcvR6G8UAzPLibg9eB47\nHtYTz+1rM4n3euK5feLECdasWTNu1hPP7ddff51AIDBu1mP39uEWAHg40H/Ztm3bAMjMzCQYDDJa\nXJYV+/1Wly5d4vvf/z5/93d/x5IlS5g6dSrnz5+PXp6amkokEmH9+vXk5+ezfPlyAFavXk1hYSFZ\nWVls3ryZAwcOAHDkyBFeeukl9u7dSyAQYN++fUyfPh2A7Oxsjh07NqQsamtrmT9//rB1Td3Sf52O\n4BauPPaLPyGGxHH0qClFp1MWhrIwnJbFwOtgV2AJl5/+7ZDL6uvrKSgoGJXHifluqO7ubpYuXcqK\nFStYsmQJ0H80cfbsWQBaW1uZNm0a0H/E0NTUFL1tc3MzXq+XjIwMmpubh+0fuM2ZM2cA6Onp4cKF\nC8OOKmJzzofynPSHIBZlYSgLQ1nYY8SysCyLVatW4ff7+fnPfx7dX1RURFVVFQBVVVXREikqKqK6\nupquri4aGxsJhULk5eWRnp5OSkoKdXV1WJbF1q1bWbx48bD72rlz56i1oIiIjJ4Ry+K9997jjTfe\n4J133mHevHnMmzePmpqa6EgpJyeHQ4cOsXnzZgD8fj/FxcX4/X4KCwupqKjAdfXLrSoqKli9ejU+\nn4/s7GwWLlwIwKpVqzh37hw+n49XXnkl+s4quT69h9xQFoayMBybhc1fJDjiCe5HHnmEvr6+6152\n8ODB6+5//vnnef7554ftv//++zlx4sSw/ZMnT2bHjh03slYREfkm+roPGUzzWENZGMrCUBb2UFmI\niEhMKosE49h57HUoC0NZGMrCHioLERGJKXHLYsjJHP19Fk6kLAxlYSgLeyRuWYiIyJhJ3LIYfGRh\n81vGxhPNYw1lYSgLQ1nYI3HLQkRExkwCl4XOWTidsjCUhaEs7JHAZSEiImMlcctiyDmL+C1jrGke\naygLQ1kYysIeiVsWIiIyZhK4LBx0ODGI5rGGsjCUhaEs7JHAZTGIg946KyISD4lbFg4tCM1jDWVh\nKAtDWdgjcctiCGcWh4jIWEngsnBmQWgeaygLQ1kYysIeCVwWgzh0JCUiMlYmRlk4iOaxhrIwlIWh\nLOyRuGXh0K8oFxGJh8QtC4fSPNZQFoayMJSFPRK4LHQ0ISIyVhK4LAZx0AluzWMNZWEoC0NZ2CNx\ny8JBBSEiEm+JWxZDOKc4NI81lIWhLAxlYY8ELgvnFISISLwlcFkM4qCRlOaxhrIwlIWhLOyRuGXh\noIIQEYm3xC2LQVwOGklpHmsoC0NZGMrCHglcFs4pCBGReEvgsnAmzWMNZWEoC0NZ2GNilIXOX4iI\n2Cpxy8KhBaF5rKEsDGVhKAt7JG5ZDOHM4hARGSsTpCycQ/NYQ1kYysJQFvYYsSyee+45PB4PgUAg\nui8SiRAMBsnJyWHBggW0t7dHLysrK8Pn85Gbm8v+/fuj+48fP04gEMDn87Fhw4bo/s7OTpYtW4bP\n5yM/P5/Tp09/u2fh0JGUiMhYGbEsnn32WWpqaobsKy8vJxgMcvLkSQoKCigvLwegoaGB7du309DQ\nQE1NDWvXrsW6+iK+Zs0aKisrCYVChEKh6H1WVlaSlpZGKBRi48aNbNq06YYX7nJoQWgeaygLQ1kY\nysIeI5bF9773PaZOnTpk3549eygtLQWgtLSUXbt2AbB7925KSkpwu91kZWWRnZ1NXV0dra2tXLx4\nkby8PABWrlwZvc3g+1q6dCm1tbXf8mk4szhERMZK8s3eoK2tDY/HA4DH46GtrQ2AlpYW8vPzo9fz\ner2Ew2Hcbjderze6PyMjg3A4DEA4HGbGjBn9C0lOZsqUKUQiEVJTU4c97rp168jMzAQgJSWFuTkz\nefLqZe9+GqYz5Wj0N4qBmeVE3B48jx0P64nn9rWZxHs98dw+ceIEa9asGTfrief266+/TiAQGDfr\nsXv7cAsAPBzov2zbtm0AZGZmEgwGGS0uyxp5nnPq1CkWLVrEiRMnAJg6dSrnz5+PXp6amkokEmH9\n+vXk5+ezfPlyAFavXk1hYSFZWVls3ryZAwcOAHDkyBFeeukl9u7dSyAQYN++fUyfPh2A7Oxsjh07\nNqwsamtrmT9//tCFd7Tz3V/+JQBXvreOjif+65+SQ8I4etSUotMpC0NZGE7LYuqW/tfLrsASLj/9\n2yGX1dfXU1BQMCqPc9PvhvJ4PJw9exaA1tZWpk2bBvQfMTQ1NUWv19zcjNfrJSMjg+bm5mH7B25z\n5swZAHp6erhw4cJ1jyqua3DHOej8hZP+EMSiLAxlYSgLe9x0WRQVFVFVVQVAVVUVS5Ysie6vrq6m\nq6uLxsZGQqEQeXl5pKenk5KSQl1dHZZlsXXrVhYvXjzsvnbu3DlqDSgiIqNrxLIoKSnh4Ycf5rPP\nPmPGjBn827/9W3SklJOTw6FDh9i8eTMAfr+f4uJi/H4/hYWFVFRU4HK5AKioqGD16tX4fD6ys7NZ\nuHAhAKtWreLcuXP4fD5eeeWV6DurbsiQownnHFnoPeSGsjCUhaEs7DHiCe6BEyXXOnjw4HX3P//8\n8zz//PPD9t9///3Rcx6DTZ48mR07dtzIOkVEJI4S+BPc1nV/nOg0jzWUhaEsDGVhjwQuCxERGSsT\npCycc2iheayhLAxlYSgLeyRuWTjo7bIiIvGWuGXhUJrHGsrCUBaGsrBHApeFMz+UJyISDwlcFs6k\neayhLAxlYSgLeyRuWVh9gzfitgwRkXHB5glL4pZFX0+8VxAXmscaysJQFoZjs7B6bb37hC0LV++g\nstA5CxFxosGvfb3dtj5UwpaF3cGMV5rHGsrCUBaGU7NwqSy+QZ+OLETE4Qa/9tk8mk/YsrC7Rccr\nx85jr0NZGMrCcGwWOrL4Bn3OLAsRketx2fyamLhlMegEt8tB74xy6jz2epSFoSwMR2Ux+LWvV2Oo\n6xoyhurtit9CRETipbdz0M86sri+QYdcrp7OEa44sTh2HnsdysJQFoaTsnD1mF+U7Z6wJG5ZDD7k\n6tGRhYg4UI+OLGIa3KKunitxXMnYctQ8NgZlYSgLw0lZDJmq6MjiGwxuUR1ZiIgTDSoLl05wf4Mh\n7wLQOQsnUhaGsjCclIVr8Jt79NbZ6xv8bihXt3PKQkQkqlvnLGIb8tZZ55SFk+axsSgLQ1kYTsrC\n1asxVGxDTnDrnIWIONCQE9w6sriuIR/K0+csHElZGMrCcFIWQ35R1hjqG3R3RH900ofyRESiBr8b\nyuqDbvs+RpCwZeHquGB+7rwYx5WMLSfNY2NRFoayMJyUxbWvfa4rF77hmn+6xC2LQaG4ujug6+s4\nrkZEZOy5Lp8but2hshjm2lBcX0fitJKx5aR5bCzKwlAWhpOySPr6mrLQkcVwSdeEknRNw4qITHSu\ny0N/SXZd+cq2x0rYsnBd+iMA1uTvAJD0VWs8lzNmnDSPjUVZGMrCcFIWA6970dfBS1/a91i23bPN\nks6fBqDb92j/9pefx3M5IiJjbtKXIQC6fY8B5nXRDolZFle+IunrCFbyrfT8Zf98clLLH+K8qLHh\npHlsLMrCUBaGU7JwdVwg6UIYa9ItdM/6HgBJEZXFEMnh/wtAryeX7uzvA+AO1UJfbzyXJSIyZpL/\nvX/c1jPjfnrvmtO/7+prox0Ssyw+/98A9PxFHn1/nk1v6kySvj6P+7ODcV6Z/Zw0j41FWRjKwnBK\nFpOP/Q6A7ruD9E6fi5V8K5PaPiXp/BlbHi/xyqLzEpPrtwHQ7X8CXC46H3oGgD97cwuur87GcXH2\nO3HiRLyXMG4oC0NZGE7I4pYP38B9shZr8nfoemA5uG+la/aT/ZfV/c6WxxwXZVFTU0Nubi4+n48X\nX3zxm6/YdZnbd/6MpK9a6Zk+l56Z/bPJzof/Ez3T5zIpcoqUVx9h8uFXSDrfNEarH1tffWXfW+MS\njbIwlIUxYbPo6SL5iyPc/t+e4fb/+V8A+Lrw77HuuBOAzr9aDcCtR36D+5P/NeoPnzzq93iTent7\n+dnPfsbBgwfJyMjgwQcfpKioiHvuuWfI9W7/78+R/MW7/Se2b7mDy//xdUi62nXJk7n07P/g9u3/\nGffn73Dbvl/Cvl/S+10vfZ576E2bSd/UTKzb/5y+29OwbpuK9WdTsW65Dcv9Z+C+DSbFPQoRcZq+\nPui5gqv7CvR04LpykaTL53B9fQ7X5QhJl78k6Vwjk/74OZPOfoqr6zIA1qRb6Cj8e7quTlUAev8i\njyvfW8etR17jjjdW0JNxHzz8j6O21Li/Qh47dozs7GyysrIA+PGPf8zu3buHlcUtJ3YB0JMxj6+X\nvkpf+tDLrTvu5NJzO0k+WcvkD98g+fPDTGpvZlJ7M+4bWIc1yR0tDiv5FpjkhqRkrKTk/p8nXf05\nyX31sklYk9z920lJ4ErCcvX/F5fr6n8H/YzLXJ7Uv32965r7GPgHrv4LXC7CdW9x66FJ0e2rP0R/\ntgZdN3pZrO2BH2Nd9zr7b/7xRk9z/Tvc8n+mj/r9JqIxzcKyAGvoz1b/tiv6s9k3bBvr6s2v3Tf0\nfl3fdPm193PNdcIfvM2t+7qH7HN9w3qH3i/D9/X14bJ6+/9KhL4+sHqht+fqvr7+/VYvrr7e/jfY\n9PX2X6evF1dfD1h9V/f39H9Tdk9nfzF0d+DquXLTX4LaO+1uuvxP0PlXq7FS7hp2eUfhL+n7zl3c\neuhlksMf39R9x+KyrGhqcbFz50727dvHv/7rvwLwxhtvUFdXxz//8z9Hr1NbWxuv5YmIJLSCgoJR\nuZ+4H1m4buA3ztF6siIi8u3E/QR3RkYGTU3mZHRTUxNerzeOKxIRkWvFvSweeOABQqEQp06doqur\ni+3bt1NUVBTvZYmIyCBxH0MlJyfzm9/8hscff5ze3l5WrVo17OS2iIjEV9yPLAAKCwv57LPP+Pzz\nz9myZcuQy274MxgTRFNTE48++iizZ89mzpw5/PrXvwYgEokQDAbJyclhwYIFtLe3R29TVlaGz+cj\nNzeX/fv3x2vptujt7WXevHksWrQIcG4O7e3t/OhHP+Kee+7B7/dTV1fn2CzKysqYPXs2gUCAp59+\nms7OTsdk8dxzz+HxeAgEAtF93+a5Hz9+nEAggM/nY8OGDTf24NY41tPTY82aNctqbGy0urq6rHvv\nvddqaGisnyQ7AAAEcElEQVSI97Js1draan300UeWZVnWxYsXrZycHKuhocH6xS9+Yb344ouWZVlW\neXm5tWnTJsuyLOuTTz6x7r33Xqurq8tqbGy0Zs2aZfX29sZt/aPtV7/6lfX0009bixYtsizLcmwO\nK1eutCorKy3Lsqzu7m6rvb3dkVk0NjZaM2fOtK5cuWJZlmUVFxdbv/vd7xyTxbvvvmvV19dbc+bM\nie67mefe19dnWZZlPfjgg1ZdXZ1lWZZVWFhovf322zEfe1yXxfvvv289/vjj0e2ysjKrrKwsjisa\ne4sXL7YOHDhg3X333dbZs2cty+ovlLvvvtuyLMt64YUXrPLy8uj1H3/8cev3v/99XNY62pqamqyC\nggLr0KFD1pNPPmlZluXIHNrb262ZM2cO2+/ELM6dO2fl5ORYkUjE6u7utp588klr//79jsqisbFx\nSFnc7HNvaWmxcnNzo/u3bdtm/fSnP435uONiDPVNwuEwM2bMiG57vV7C4XAcVzS2Tp06xUcffcRD\nDz1EW1sbHo8HAI/HQ1tbGwAtLS1D3j02kTLauHEjL7/8MklJ5n9TJ+bQ2NjInXfeybPPPsv8+fP5\nyU9+wuXLlx2ZRWpqKn/zN39DZmYm06dP57vf/S7BYNCRWQy42ed+7f6MjIwbymRcl8WNfAZjorp0\n6RJLly7l1Vdf5Tvf+c6Qy1wu14jZTITc3nzzTaZNm8a8efOwvuFzo07IAaCnp4f6+nrWrl1LfX09\nt99+O+Xl5UOu45QsvvjiC1555RVOnTpFS0sLly5d4o033hhyHadkcT2xnvufYlyXhVM/g9Hd3c3S\npUtZsWIFS5YsAfp/Yzh7tv8bdVtbW5k2bRowPKPm5mYyMjLGftGj7P3332fPnj3MnDmTkpISDh06\nxIoVKxyXA/T/Ruj1ennwwQcB+NGPfkR9fT3p6emOy+LDDz/k4YcfJi0tjeTkZH74wx/y+9//3pFZ\nDLiZPxNer5eMjAyam5uH7L+RTMZ1WTjxMxiWZbFq1Sr8fj8///nPo/uLioqoqqoCoKqqKloiRUVF\nVFdX09XVRWNjI6FQiLy8vLisfTS98MILNDU10djYSHV1NY899hhbt251XA4A6enpzJgxg5MnTwJw\n8OBBZs+ezaJFixyXRW5uLh988AEdHR1YlsXBgwfx+/2OzGLAzf6ZSE9PJyUlhbq6OizLYuvWrdHb\njGg0TrjY6a233rJycnKsWbNmWS+88EK8l2O7I0eOWC6Xy7r33nut++67z7rvvvust99+2zp37pxV\nUFBg+Xw+KxgMWufPn4/e5h/+4R+sWbNmWXfffbdVU1MTx9Xb4/Dhw9F3Qzk1h48//th64IEHrLlz\n51pPPfWU1d7e7tgsXnzxRcvv91tz5syxVq5caXV1dTkmix//+MfWXXfdZbndbsvr9Vq//e1vv9Vz\n//DDD605c+ZYs2bNstavX39Djx33LxIUEZHxb1yPoUREZHxQWYiISEwqCxERiUllISIiMaksREQk\nJpWFiIjE9P8Bu5w1zgBX2aQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e524210>"
       ]
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, it is perfectly mirrored at the half. So let's just take the first half."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Amplitude Spectrum"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Remember: $N$ is half the length of the output of the FFT."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(np.abs(Y[:N]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 88,
       "text": [
        "[<matplotlib.lines.Line2D at 0x110008690>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FoSwMZeEeFYSIiMSlgkgymq8aysJQFoaycI8KQkRE4lJBJBnNVw1lYSgLQ1m4x9KC8CT6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\nvSEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f762910>"
       ]
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That looks pretty good. It is called the **amplitude spectrum** of the time domain signal and was calculated with the Discrete Fourier Transform with the *Chuck-Norris-Fast* FFT algorithm. But how to get the x- and y-axis to real physical scaled values?!"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Real Physical Values for the Amplitude and Frequency Axes of the FFT"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "x-Axis: The Frequency Axis of the FFT"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, let us determine the timestep, which is used to sample the signal. We made it synthetically, but a real signal has a period (measured every second or every day or something similar). If there is no constant frequency, the FFT can not be used! One can interpolate the signal to a new time base, but then the signal spectrum is not the original one. It depends on the case, if the quality is enough or if the information is getting lost with this shift keying. Enough.\n",
      "\n",
      "We have a good signal:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dt = t[1] - t[0]\n",
      "fa = 1.0/dt # scan frequency\n",
      "print('dt=%.5fs (Sample Time)' % dt)\n",
      "print('fa=%.2fHz (Frequency)' % fa)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dt=0.00629s (Sample Time)\n",
        "fa=159.00Hz (Frequency)\n"
       ]
      }
     ],
     "prompt_number": 89
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we need to create a x-Axis vector, which starts from $0.0$ and is filled with $N$ (length of half of the FFT signal) values and going all the way to the maximum frequency, which can be reconstructed. This frequency is half of the maximum sampling frequency ($f_a$) and is called the `Nyquist-Frequency` (see [Nyquist-Shannon Sampling Theorem](http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem))."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = np.linspace(0, fa/2, N, endpoint=True)\n",
      "X[:4]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 90,
       "text": [
        "array([ 0.        ,  0.15899579,  0.31799158,  0.47698736])"
       ]
      }
     ],
     "prompt_number": 90
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's plot the amplitude spectrum over the newly created frequency vector $X$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(X, np.abs(Y[:N]))\n",
      "plt.xlabel('Frequency ($Hz$)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 91,
       "text": [
        "<matplotlib.text.Text at 0x10f02da90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FMO+W9vvdEUlLeOsV0cbt/TH6hHf8FdoHI7QPhLX9tzdGaG8c5+tw1NdAaB+M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\nURAREdP/B6JLMLuZPUtEAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f02b990>"
       ]
      }
     ],
     "prompt_number": 91
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Yeah! The x-Axis is showing us, that we have a peak at exactly these frequencies, from which our synthetically created signal was build of. That was the job.\n",
      "\n",
      "The sample frequency was $f_a=159Hz$, so the amplitude spectrum is from $0.0$ to $\\frac{f_a}{2}=79.5Hz$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "y-Axis: The Amplitude of the FFT Signal"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This task is not this easy, because one have to understand, how the Fourier Transform or the Discrete Fourier Transform works in detail. We need to transform the y-axis value from *something* to a real physical value. Because the power of the signal in time and frequency domain have to be equal, and we just used the left half of the signal (look at $N$), now we need to multiply the amplitude with the factor of **2**. If we inverse the FFT with `IFFT`, the power of the signal is the same.\n",
      "\n",
      "But that was the easy part. The more complicated one is, if you look at the definition of the Discrete Fourier Transform:\n",
      "\n",
      "$Y[k]=\\frac{1}{N} \\underbrace{\\sum_{N} x(nT)\\cdot e^{-i 2 \\pi \\frac{k}{N}n}}_{DFT}$\n",
      "\n",
      "In most implementations, the output $Y$ of the `FFT` is normalized with the number of samples. We have to divide by $N$ to get the real physical value.\n",
      "\n",
      "The magic factor is $\\frac{2}{N}$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(X, 2.0*np.abs(Y[:N])/N)\n",
      "plt.xlabel('Frequency ($Hz$)')\n",
      "plt.ylabel('Amplitude ($Unit$)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 92,
       "text": [
        "<matplotlib.text.Text at 0x10f6dd890>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HPQ+hYRc+TnQ/jj+5nhZZS2j5xbuEFG2nxVcZ8FVGve2qr7iK6vDOWOGdqA5r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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1100291d0>"
       ]
      }
     ],
     "prompt_number": 92
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Yeah! Job accomplised. Congratulations. But wait...\n",
      "\n",
      "If you look at the parameters for the original signal ($A$), our signal amplitude was not, what is calculated here. Why??"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The wrong Amplitude Spectrum because of Leakage Effect"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Take a look at the original signal."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(t,s)\n",
      "plt.xlabel('Time ($s$)')\n",
      "plt.ylabel('Amplitude ($Unit$)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 93,
       "text": [
        "<matplotlib.text.Text at 0x10f764650>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yij3AWYU6vrj9JbwfAKpDRvzGrbtR7AGWiPhnXw3wFQL++X0o9ABnCvp3PL8H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\n/wErWRpk12kqcQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10fd69a90>"
       ]
      }
     ],
     "prompt_number": 93
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Do you see, that the signal do not end at amplitude zero, where it started? That means, if you add these signals up, it looks like this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(t, s, label='Signal 1')\n",
      "plt.plot(t+t[-1], s, label='Signal 1 again')\n",
      "plt.xlim(t[-1]-1, t[-1]+1)\n",
      "plt.xlabel('Time ($s$)')\n",
      "plt.ylabel('Amplitude ($Unit$)')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 94,
       "text": [
        "<matplotlib.legend.Legend at 0x1105ecf10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/JHw+Kk3ijR1aB8Dg++psXa9ilrYJPdf6PKZW1xb/PDnObyh1DHt3AmF/FTAH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\nKP4fOq2AjcbSRIYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f78bb50>"
       ]
      }
     ],
     "prompt_number": 94
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And the Fourier Transform was originally invented by Mr Fourier for, and only for, periodic signals (see [Fourier Transform](http://en.wikipedia.org/wiki/Fourier_transform)). So the Discrete Fourier Transform does and the Fast Fourier Transform Algorithm does it, too.\n",
      "\n",
      "The signal has to be strictly periodic, which introduces the so called **windowing** to eliminate the leakage effect."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Window Functions to get periodic signals from real data"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are a lot of window functions, like the *Hamming*, *Hanning*, *Blackman*, ..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hann = np.hanning(len(s))\n",
      "hamm = np.hamming(len(s))\n",
      "black= np.blackman(len(s))\n",
      "\n",
      "plt.figure(figsize=(8,3))\n",
      "plt.subplot(131)\n",
      "plt.plot(hann)\n",
      "plt.title('Hanning')\n",
      "plt.subplot(132)\n",
      "plt.plot(hamm)\n",
      "plt.title('Hamming')\n",
      "plt.subplot(133)\n",
      "plt.plot(black)\n",
      "plt.title('Blackman')\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aTdGQpvXa+YjFewna+z/kIbNV0dQb06dPZ/r06TUeW7hwofv/nTt35rPPPlPb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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1105cf410>"
       ]
      }
     ],
     "prompt_number": 95
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "All have different characteristics, which is an [own engineering discipline](http://en.wikipedia.org/wiki/Window_function). Let's take the *Hanning* window function to multiply our signal with."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(t,hann*s)\n",
      "plt.xlabel('Time ($s$)')\n",
      "plt.ylabel('Amplitude ($Unit$)')\n",
      "plt.title('Signal with Hanning Window function applied')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 96,
       "text": [
        "<matplotlib.text.Text at 0x1107829d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MmSiae1E3V/NXJrH87gOxP35WOMrEwQWFPHmFMjqK2zbcXJQf0Li5mDkTLQFO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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x110519510>"
       ]
      }
     ],
     "prompt_number": 96
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "FFT with windowed signal"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Yhann = np.fft.fft(hann*s)\n",
      "\n",
      "plt.figure(figsize=(7,3))\n",
      "plt.subplot(121)\n",
      "plt.plot(t,s)\n",
      "plt.title('Time Domain Signal')\n",
      "plt.ylim(np.min(s)*3, np.max(s)*3)\n",
      "plt.xlabel('Time ($s$)')\n",
      "plt.ylabel('Amplitude ($Unit$)')\n",
      "\n",
      "plt.subplot(122)\n",
      "plt.plot(X, 2.0*np.abs(Yhann[:N])/N)\n",
      "plt.title('Frequency Domain Signal')\n",
      "plt.xlabel('Frequency ($Hz$)')\n",
      "plt.ylabel('Amplitude ($Unit$)')\n",
      "\n",
      "plt.annotate(\"FFT\",\n",
      "            xy=(0.0, 0.1), xycoords='axes fraction',\n",
      "            xytext=(-0.8, 0.2), textcoords='axes fraction',\n",
      "            size=30, va=\"center\", ha=\"center\",\n",
      "            arrowprops=dict(arrowstyle=\"simple\",\n",
      "                            connectionstyle=\"arc3,rad=0.2\"))\n",
      "plt.tight_layout()\n",
      "\n",
      "plt.savefig('FFT.png',bbox_inches='tight', dpi=150, transparent=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2uv2iUCi1jGuVc5pjp1CMOJRj37Vrl8st90hz7JSGRlVz7HWxnMvm2Pctgfr4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\niUTSiZCJXSKRSCSSTsT/B+QtmCM0fBxuAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11068e590>"
       ]
      }
     ],
     "prompt_number": 97
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is exactly, what we wanted to see: A beautiful amplitude spectrum of our signal, which was calcualted with the FFT algorithm.\n",
      "\n",
      "Now let's take a look at some real data!"
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Vertical Grid Load of Germany 2013"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\"The vertical grid load is the sum, positive or negative, of all power transferred from the transmission grid through directly connected transformers and power lines to distribution grids and final consumers.\"\n",
      "\n",
      "Download the Data from [50Hertz.com](http://www.50hertz.com/de/1987.htm)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!wget -O 'Vertikale_Netzlast_2013.csv' 'http://www.50hertz.com/transmission/files/sync/Netzkennzahlen/Netzlast/ArchivCSV/Vertikale_Netzlast_2013.csv'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "--2014-04-29 14:21:02--  http://www.50hertz.com/transmission/files/sync/Netzkennzahlen/Netzlast/ArchivCSV/Vertikale_Netzlast_2013.csv\r\n",
        "Resolving www.50hertz.com... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "95.100.62.102\r\n",
        "Connecting to www.50hertz.com|95.100.62.102|:80... connected.\r\n",
        "HTTP request sent, awaiting response... "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "200 OK\r\n",
        "Length: unspecified [text/comma-seperated-values]\r\n",
        "Saving to: \u2018Vertikale_Netzlast_2013.csv\u2019\r\n",
        "\r\n",
        "\r",
        "    [<=>                                    ] 0           --.-K/s              "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "    [ <=>                                   ] 517,387     2.45MB/s             "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "    [  <=>                                  ] 980,895     3.24MB/s   in 0.3s   \r\n",
        "\r\n",
        "2014-04-29 14:21:03 (3.24 MB/s) - \u2018Vertikale_Netzlast_2013.csv\u2019 saved [980895]\r\n",
        "\r\n"
       ]
      }
     ],
     "prompt_number": 98
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df = pd.read_csv('Vertikale_Netzlast_2013.csv', header=6, sep=';', parse_dates=[[0, 1]], index_col=0, na_values=['n.v.'])\n",
      "df.rename(columns={'Unnamed: 3': 'Load'}, inplace=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 99
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Interpolate the missing data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df.Load = df.Load.interpolate()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 100
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(14,5))\n",
      "df.Load.plot()\n",
      "plt.title('Vertical Grid Load Germany 2013')\n",
      "plt.ylabel('Power [$MW$]')\n",
      "plt.savefig('VerticalGridLoadGermany2013.png',bbox_inches='tight', dpi=150, transparent=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SVk0Ts0Y9BgCQFTZyuf3/hNx3Wtnz1hOuTIkLYyf6gsiZHU/HCBljF5FmiH6I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WIFAOCVV17BnDlzEAwG0aNHD/Tq1QubNm3C8ePHUVtbixEjErdbc+fOTeehQuZWlRHUMwX/15+K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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x110537b50>"
       ]
      }
     ],
     "prompt_number": 101
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Do the FFT"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hann = np.hanning(len(df.Load.values))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 102
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Y = np.fft.fft(hann*df.Load.values)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 103
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = len(Y)/2+1\n",
      "fa = 1.0/(15.0*60.0) # every 15 minutes\n",
      "print('fa=%.4fHz (Frequency)' % fa)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "fa=0.0011Hz (Frequency)\n"
       ]
      }
     ],
     "prompt_number": 104
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = np.linspace(0, fa/2, N, endpoint=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 105
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(X, 2.0*np.abs(Y[:N])/N)\n",
      "plt.xlabel('Frequency ($Hz$)')\n",
      "plt.ylabel('vertical powergrid load ($MW$)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 106,
       "text": [
        "<matplotlib.text.Text at 0x110734bd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4+vry+uuvU1paarKCKisrCQkJITIyEoCSkhIiIiLw9/dn6NChtRZZxMfH4+fn\nR9euXdm8ebM+fujQIQIDA/Hz82PWrFkmq00IIYT5GdWYpk2bxvbt21m4cCEHDhxg4cKF7Nixg2nT\nppmsoAULFhAQEKDfFTchIYGIiAhOnTrFkCFDSEhIACAzM5PVq1eTmZlJeno606dPp2bnb9q0aSQl\nJZGVlUVWVhbp6em//oGK7jCqPs8t+WyXytlA/XyWYFRjWrduHRs2bGD48OF0796d4cOHs379etat\nW2eSYvLy8khLSyM2NlZvMuvXrycmJgaAmJgY/bNSU1MZP348jo6O+Pj44OvrS0ZGBoWFhVy5coXQ\n0FAAoqOjTVafEEII8zNq8UO7du24fv06zs7O+tiNGzdo3769SYqZPXs27777LpcvX9bHiouLcXNz\nA8DNzY3i4mIACgoKCA8P11/n6elJfn4+jo6OeHp66uMeHh7k5+ff8fMmb4f2FZ9T1eYQTk5OBAYG\n6te5qvnWY6uPa8aspR7JJ/lqHvfv39+q6pF8d3+8e/duVq1aBYC3tzcRERGYm1GLHxISEli5ciUz\nZszAy8uLc+fOkZiYyIQJE+jbt6/+usGDBxtdyMaNG9m0aRN///vf2bFjB/Pnz2fDhg04Oztz8eJF\n/XUuLi6UlJQwc+ZMwsPDmThxIgCxsbEMHz4cHx8f4uLi2LJlCwC7du1i3rx5bNiwodbn6YsfJq+h\nostvja5XCCEaI0ssfjBqj2nx4sVA9aKDGpqmsXjxYv05gOzsbKML2bt3L+vXryctLY3S0lIuX77M\npEmTcHNzo6ioCHd3dwoLC3F1dQWq94Ryc3P19+fl5eHp6YmHhwd5eXm1xj08PIyux9bd+m1bRZLP\ndqmcDdTPZwlGHWPKyckhJyeH7Oxs/dd/Pr6XpgTwl7/8hdzcXLKzs0lJSWHw4MEkJyczcuRIli1b\nBsCyZcsYPXo0UH1vqJSUFMrLy8nOziYrK4vQ0FDc3d1xcnIiIyMDTdNITk7W33NHii5+EEIIW2XU\nHpMl1azKi4uLIyoqiqSkJHx8fFizZg0AAQEBREVFERAQgIODA4mJifp7EhMTmTx5Mjdu3GDEiBEM\nGzaswXI0FNW/sUk+26VyNlA/nyXICbYxq6noav6DeUIIoQKrO8FW2A7Vz6WQfLZL5Wygfj5LkMYk\nhBDCqtR5jGnr1q36sZu7uZcl4sJ8VJ/nlny2S+VsoH4+S6izMU2dOrVejeleV+M1vEZ5iE0IIaxW\nnVN5d1r/0zSXAAAYs0lEQVQOfqdfwrqoPs8t+WyXytlA/XyWYPRy8eLiYvbv38+FCxe4dUHflClT\nTFqYEEKIxsmoxrRu3TqeeeYZ/Pz8OH78OD169OD48eP0799fGpOVUX2eW/LZLpWzgfr5LMGoVXl/\n+MMf+PTTTzly5AgtWrTgyJEjfPTRR/Tq1ctc9QkhhGhkjGpMubm5REVF6Y81TSM6Oprly5ebvDBL\nMSh6frHq89ySz3apnA3Uz2cJRjUmV1dXioqKAPDx8eHbb7/lzJkzVFVVmaU4IYQQjY9RjSk2Nlb/\nNjB79mwGDx5McHCwSe9gK0xD9XluyWe7VM4G6uezBKMWP8TFxem/j46OZuDAgVy7do2AgACTFyaE\nEKJxuq9LEnXo0EGakpVSfZ5b8tkulbOB+vkswajGNHPmTPbs2VNrbO/evbz44osmLUoIIUTjZdRt\nL9q0aUN+fj5NmzbVx0pLS/Hy8uL8+fNmKdBcam57cTV6JTe7Nb77NQkhxL2wutte2NnZ3bYCr6qq\nikZ6SychhBBmYFRj6t+/P6+//rrenCorK3nzzTcZMGCAWYoT9071eW7JZ7tUzgbq57MEo1blLViw\ngMcffxx3d3c6dOjAuXPnaNeuHRs2bDBXfUIIIRoZo2+tXllZyf79+8nNzcXb25vQ0FDs7GzvfoNy\njEkIIYxniWNMde4xffPNNzz88MNA7ZsGtmnThuvXr7Njxw7Ahm8UKMfHhBDCqtTZmKZPn87x48eB\nu980UO7JZF12796t9Bnoks92qZwN1M9nCXU2ppqmBNU3DRRCCCHMyaiDQ++9994dx99//32TFCNM\nR/VvbJLPdqmcDdTPZwlGNaa33377juPvvPOOSYoRQggh6rVcfNu2bWiaRmVlJdu2bav13JkzZ3By\ncjJLceLeqT7PLflsl8rZQP18llCvxjRlyhQMBgNlZWVMnTpVHzcYDLi5ubFw4UKzFWh+sipPCCGs\nSb0aU82ihwkTJrBy5Upz1iNMRPVvbJLPdqmcDdTPZwn1PsZUUVHB2rVrKSsrM2c9QgghGrl6NyYH\nBwe6dOnChQsXzFmPMBHVr9cl+WyXytlA/XyWYNSqvIkTJxIZGcnSpUvZunUr27Zt03+ZQm5uLoMG\nDaJ79+706NGDv/3tbwCUlJQQERGBv78/Q4cO5dKlS/p74uPj8fPzo2vXrmzevFkfP3ToEIGBgfj5\n+TFr1iyT1CeEEML8jLpWno+PT/Wb7nD1B1Nc+aGoqIiioiJ69uzJ1atX6d27N+vWrWPJkiW0adOG\nV155hblz53Lx4kUSEhLIzMxkwoQJHDhwgPz8fH7729+SlZWFwWAgNDSUDz/8kNDQUEaMGMELL7zA\nsGG/XBNPv1beM8nc7P7YfdcuhBCNgVVcK+9W5r7yg7u7O+7u7gC0aNGCbt26kZ+fz/r169m5cycA\nMTExPPLIIyQkJJCamsr48eNxdHTEx8cHX19fMjIy6NChA1euXCE0NBSA6Oho1q1bV6sxCSGEsE5G\nNSaAzZs3k5KSwo8//sjGjRs5ePAgly9fNvlFXHNycjhy5AhhYWEUFxfj5uYGgJubG8XFxQAUFBQQ\nHh6uv8fT05P8/HwcHR3x9PTUxz08PMjPz7/tMyZvh/bla6lyPY6TkxOBgYH6ipqaeWJbfbxo0SKl\n8kg+66rvfh7fegzGGuqRfHXnWbVqFQDe3t5ERERgbkZN5S1cuJAPPviA2NhY4uPjuXz5MsePH+f5\n559n7969Jivq6tWrDBw4kDfeeIPRo0fj7OzMxYsX9eddXFwoKSlh5syZhIeHM3HiRABiY2MZPnw4\nPj4+xMXFsWXLFgB27drFvHnzat03SvWpPNVP8pN8tkvlbKB+Pqu7tfpf//pXvv76a+bMmYO9vT0A\n3bp147vvvjNZQTdv3mTMmDFMmjSJ0aNHA9V7SUVFRQAUFhbi6uoKVO8J5ebm6u/Ny8vD09MTDw8P\n8vLyao17eHiYrEZboPJ/DJB8tkzlbKB+PkswqjFdvXoVLy+vWmPl5eU0bdrUJMVomsbUqVMJCAjg\nxRdf1MdHjhzJsmXLAFi2bJnesEaOHElKSgrl5eVkZ2eTlZVFaGgo7u7uODk5kZGRgaZpJCcn6+8R\nQghh3YxqTAMGDCAhIaHW2MKFCxk0aJBJitmzZw8rVqxg+/bthISEEBISQnp6uj4t5+/vz7Zt24iL\niwMgICCAqKgoAgICGD58OImJifqKwcTERGJjY/Hz88PX1/cuCx/UvCSR6udSSD7bpXI2UD+fJRi1\n+GHhwoVERkby8ccfc/XqVfz9/WnZsiUbN240STH9+/enqqrqjs99/fXXdxx/7bXXeO21124b7927\nN8eOHTNJXUIIISzHqMUPAFVVVRw4cICzZ8/i7e1NaGgodnZG7XhZhV8WPyznZvfHG7ocIYSwCVZ3\nHtOsWbOYOHEiYWFhhIWFmasmIYQQjZjRuzqjR4/G19eXN998k++//94cNQkTUH2eW/LZLpWzgfr5\nLMGoxrRgwQJyc3NZtGgR586dIzw8nN69ezN//nxz1Wd+xs1kCiGEMDOjjzHdKj8/n8mTJ7N169Zf\nXbRgrfRjTBOXcbNHZEOXI4QQNsHqTrCF6nOZkpOTGTFiBH5+fjg6OrJ8+XJz1CaEEKIRMqoxPfXU\nU7i5ufHRRx8RGRnJ2bNnSUtL45lnnjFXfeIeqT7PLflsl8rZQP18lmDUqrw+ffowf/58vL29zVWP\nEEKIRu6+jjHZMjnGJIQQxrPKY0zqaZR9WQghrJY0JiPY5/8Lx8y0hi6jXlSf55Z8tkvlbKB+Pkto\n9I3J4Uz9/xE5fTiYFsnPYFdy1owVCSFE49boG1OzfZ9gdzG37hfewnDlRzNVYzqq3xNG8tkulbOB\n+vksodE3JgDDT7ffdl0IIUTDkMYEYFDvj0H1eW7JZ7tUzgbq57ME9X4i34ufby4ohBCi4UljAiX3\nmFSf55Z8tkvlbKB+PktQ7yfyvVCwMQkhhK2Sn8hwD1N51n9Srurz3JLPdqmcDdTPZwnSmED2mIQQ\nworIT2Sg+aa3GroEk1N9nlvy2S6Vs4H6+SxBGhPgeHoHhhuXGroMIYQQSGP6RWVFQ1dgUqrPc0s+\n26VyNlA/nyVIY9LdsqCh7Ao0zruBCCFEg5PGVEOrAsAh+1uc3+pA8w1xDVzQ/VF9nlvy2S6Vs4H6\n+SxBGlONn/eQmu5aCECzbz9uyGqEEKLRksb0M8PNGzyQ8jxNTqY3dCkmofo8t+SzXSpnA/XzWYI0\npp+1eq83Tf/9hcm3a7iU3yD3bzp27JjFP9OSJJ/tUjkbqJ/PEpRuTOnp6XTt2hU/Pz/mzp1r9PsN\nl/LuOO5wdn+9F0c8ODeQVu+GQEW50Z9/Py5fvmzRz7M0yWe7VM4G6uezBGUbU2VlJTNmzCA9PZ3M\nzExWrVrFyZMnjdrGg3ODcDz6D5qnvkyr+B76+AOb/i8tFz9a/aCqCscT/6T5xtdouuf/Qfn1XzZw\ny+8NZVfvUOTNO35uk8MpOGZuMqpWIYRQhUNDF2Au+/fvx9fXFx8fHwDGjRtHamoq3bp1M2o7LVZN\nveO4w7mDOM9xuW38gY1z7vj6B//kW+dnVT7ohf2lX+6mWxY8lkrvPlB5E7uf8mm2Z7H+3PXhb2Nf\nkkNVC1cq23TG8Yfd2OcepPSR/0H7Lxdyj+/H4bvNND34GRjsuNltGFWt2sHNMrB3AIdmUFFafZ1A\ng32tOuxKcnD4YTdl4VOrn9fAUFmGofQymmNzcGiKZudYvZLRzk7fezTcuITWrNUtYwYMlWU0+dcX\n3OzUnyoXn58/Qat+/h5uN2KorMBQepncEwdx+GEP+jL/qgrsLvxAZfugn8d+3rZWBZqGoaoCzaFp\n9XNV1XUbSi9j/+P3VHiH1q5H07D/3zNozR+EynKqnNrdcjaB9svessEAWlX1tu2bYHcpD+0BZ7Sm\nLTFUlILBHs3OgdrXVjT8/Dmavrlaj3+We/Iw9ucO/FxXzffHn3+vaT/XUXuzd3xg+Pnzqqp+edzA\nck8ewT73UP1ebNWnbdy5Nv3vrgFVunWDpi0atIb7YdA0q/6bv2dffPEFX331FR9/XL26bsWKFWRk\nZLBwYfWqu61btzZkeUIIYbOGDBli1u0ru8dkqOObobn/YIUQQtwbZY8xeXh4kJv7y7RYbm4unp6e\nDViREEKI+lC2MfXp04esrCxycnIoLy9n9erVjBw5sqHLEkIIUQdlp/IcHBz48MMPefTRR6msrGTq\n1KlGL3wQQghheTa9x1TXeUrDhw/n0UcfxWAwkJKSwpEjR+p8b0lJCREREfj7+zN06FAuXfrldhjx\n8fH4+fnRtWtXNm/ebN5wd6nxVi+88AJ+fn4EBwffV76SkhIGDRpEy5YtmTlzpnmD1VHjrUyVb8uW\nLfTp04egoCD69OnD9u3blcm2f/9+QkJCCAkJISgoiNWrV5s1291qvJWp8tU4d+4cLVq0YP78+eYJ\ndQtL5svJyaF58+b63+H06dPNG+4uNd7KlH9/R48epV+/fvTo0YOgoCDKysruXqBmoyoqKrTOnTtr\n2dnZWnl5uRYcHKxlZmbWes0///lPbfjw4Zqmadq+ffu0sLCwOt/78ssva3PnztU0TdMSEhK0V199\nVdM0TTtx4oQWHByslZeXa9nZ2Vrnzp21yspKZfJdu3ZN2717t7Z48WJtxowZZsvVUPmOHDmiFRYW\napqmacePH9c8PDyUyXb9+nX932JhYaHWunVrraKiQpl8NcaMGaNFRUVp7733ntmyNUS+7OxsrUeP\nHmbNdCtL57t586YWFBSkHT16VNM0TSspKanzZ6fN7jHdep6So6Ojfp7SrdavX09MTAwAYWFhXLp0\niaKioru+99b3xMTEsG7dOgBSU1MZP348jo6O+Pj44Ovry/79+5XJ98ADD/DQQw/RtGlTs2VqyHw9\ne/bE3d0dgICAAG7cuMHNm3c+wdnWsjVv3hw7u+r/yjdu3KBVq1bY29c+N82W8wGsW7eOTp06ERAQ\nYLZcDZnPkiydb/PmzQQFBREYGAiAs7Oz/u/119hsY8rPz8fLy0t/7OnpSX5+fr1eU1BQ8KvvLS4u\nxs3NDQA3NzeKi4sBKCgoqLWq706fZ0qWzlejrmX2ptJQ+QC+/PJLevfujaOjo0kz1VV3fV5zr9n2\n799P9+7d6d69O++//75ZctVVe31ecy/5rl69yrx583jrrbfMFaletdfnNff695ednU1ISAiPPPKI\n2S8Ca+l8p06dwmAwMGzYMHr37s27775bZ402u/ihvj9AtXqcP6xp2h23ZzAY7vo55vwhbg35zKmh\n8p04cYK4uDi2bNlSv0LvQUNkCw0N5cSJE3z33XcMGzaMRx55hFatWtW/aCNYOt9bb73F7NmzeeCB\nB+q1zftl6Xzt27cnNzcXZ2dnDh8+zOjRozlx4gQtW7Y0rvB6snS+iooKdu/ezcGDB2nevDlDhgyh\nd+/eDB48+Fe3a7N7TPU5T+k/X5OXl4enp+cdxz08PIDqTl9UVARAYWEhrq6uv7qtmveYg6XzWVpD\n5MvLy+PJJ58kOTmZjh07miXXneq25N9d165d6dy5M6dPnzZpprvVbu58+/fv55VXXqFjx44sWLCA\nv/zlLyQmJiqTr0mTJjg7OwPQq1cvOnfuTFZWlnnC3aF2c+fz8vLi4YcfxsXFhebNmzNixAgOHz58\n9yLv4xhag7p586bWqVMnLTs7WysrK6vzAN63336rH8C723tffvllLSEhQdM0TYuPj79t8UNZWZn2\nww8/aJ06ddKqqqqUyVdjyZIlFln8YOl8Fy9e1IKCgrR//OMfymXLzs7Wbt68qWmapuXk5GheXl7a\nTz/9pEy+W7311lva/PnzzZatrhprmDLf+fPn9cUqZ86c0Tw8PLSLFy8qk6+kpETr1auXdv36de3m\nzZvab3/7Wy0tLe2uNdpsY9I0TUtLS9P8/f21zp07a3/5y180TdO0xYsXa4sXL9Zf89///d9a586d\ntaCgIO3QoUN3fa+madr//u//akOGDNH8/Py0iIiIWv9A/vznP2udO3fWunTpoqWnpyuXr0OHDpqL\ni4vWokULzcvLSzt58qQy+d555x3tv/7rv7SePXvqv86fP69EtuTkZK179+5az549tb59+2qbNm0y\nW66GyHcrSzSmX6vRXPm+/PJL/e+vV69e2saNG5XKp2matmLFCq179+5ajx497viF4z8pexFXIYQQ\ntslmjzEJIYRQkzQmIYQQVkUakxBCCKsijUkIIYRVkcYkhBDCqkhjEkIIYVWkMQnRyMyZM4cFCxaY\nbHthYWFkZmaabHtCyHlMolHw8fHhxx9/1K+6bTAYOHXqlH7F8cbi/PnzhISEcObMGZNdSf7zzz9n\n9erVfPHFFybZnhCyxyQaBYPBwMaNG7ly5QpXrlzh8uXLtzWlioqKBqrOcpYuXcpjjz12W1PKyMjg\n0UcfpX///qxcuRKA5ORkWrduzcyZM+96i5fIyEi2b99+xyu5C3EvpDGJRs3Hx4d58+YRFBREy5Yt\nqaqqoqCggDFjxuDq6kqnTp1YuHBhrfccOXKEXr164eTkxLhx4xg3bhxvvPEGAHZ2dvzwww/6aydP\nnqw/B9x12z4+PsyfP5/g4GAefPBBxo0bV+tOn7m5uTz55JO4urrSpk0b/U7D7777LmPHjq1V4wsv\nvMCLL754W9709HQGDhx423hYWBjNmjXj97//PRMmTABgxIgRlJaWMn/+fEJDQ3/1z7BZs2b07t2b\nr7766ldfI4QxpDGJRuPXZq1TUlLYtGmTfivoyMhIQkJCKCgoYOvWrXzwwQds3rwZgPLyckaPHk1M\nTAwXL17kqaeeYu3atb96K4FbL/9fVVV1121D9bTYV199RXZ2NkePHmXp0qUAVFZW8vjjj9OxY0fO\nnj1Lfn4+48aNA2DSpEmkp6fz008/AdV7fqtXr9Zv2narY8eO0aVLl9vGKysr+fbbbxkyZIg+tnnz\nZsLCwmjSpMld/1wBunXrxr///e86XydEfdjs/ZiEMIamaYwePRoHh+p/8oMGDdIbygsvvKBfuj8j\nI4MLFy7w+uuvA9CxY0diY2NJSUlh6NCh7Nu3j4qKCmbNmgXAmDFj6Nu3b52fDXDgwIG7brumlpop\nxsjISP71r38B1bd+KCws5N1339Xv/vnQQw8B4O7uzoABA/j888+JjY0lPT2dtm3bEhISclstly5d\nuuN9fg4fPoyLiwtr167Vxz755BOGDh2qP969ezd/+tOf8Pb2xs7OjmHDhjF69GgAWrZsSWFh4V3/\nHISoL2lMolEwGAykpqbe8eZkt96R8+zZsxQUFOj3x4HqvYmHH34YqJ6K+8/7cHXo0KHOz67PtoFa\nx72aN29OQUEBUD2N16FDh1+9JXVMTAyLFy8mNjaWFStWMGnSpDu+ztnZmStXrtw2vm3bNp5++ula\ne1lvvvkmgwYN0h/379+f9PR0EhMTOXXqlN6UAC5fvlwrlxD3Q6byRKN36zSct7c3HTt25OLFi/qv\ny5cvs3HjRgDatWt3222oz549q//+gQce4Pr16/rjW/civLy87rrtu/Hy8uLcuXNUVlbe8flRo0Zx\n9OhRjh8/zj//+U8mTpx4x9cFBQXx/fff3za+Y8cOfQ8Mqm8Ad/78ecLDw2u97s9//jM//PADH3zw\nQa3xkydPEhwcXGcOIepDGpMQtwgNDaVly5bMmzePGzduUFlZyfHjxzl48CAA/fr1w8HBgb/97W/c\nvHmTtWvXcuDAAf39PXv25LPPPqOyspL09HS++eabem+7rrratWtHXFwc169fp7S0lL179+rPN2/e\nnDFjxjBhwgTCwsJuuyNpjREjRrBz585aYzdv3mTv3r3069dPH9u1axe/+c1v9KlPgPj4eOzs7Hjv\nvfc4ceIEFy5cAKC0tJTDhw8TERFRZw4h6kMakxC3sLOzY+PGjfzrX/+iU6dOtG3blueff57Lly8D\n1bfBXrt2LUuXLqV169asWbOGJ598Uj+OtGDBAjZs2ICzszMrV67kiSee0Ldtb29/123/p1sXTtjb\n27NhwwZOnz6Nt7c3Xl5erFmzptbrY2JiOH78+K9O4wFER0eTlpZGaWkpUL3CMC4uDoPBoB9fSklJ\n4e9//zuVlZV689u7dy/BwcE89NBDDB48mH/84x+0adMGgA0bNjBo0KBGd06YMB85wVaI+/Tss8/i\n6enJO++806B15Obm0rVrV4qLi2nRosWvvu4Pf/gDrq6u+gKO+xUeHs6nn35KQECASbYnhCx+EOI+\nWcN3u6qqKubPn8/48ePv2pSg+jiRKe3bt8+k2xNCGpMQ9+nWKbeGcO3aNdzc3OjYsSPp6ekNVocQ\npiJTeUIIIayKLH4QQghhVaQxCSGEsCrSmIQQQlgVaUxCCCGsijQmIYQQVkUakxBCCKsijUkIIYRV\nkcYkhBDCqvx/n3oVD2AgdSEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11067e810>"
       ]
      }
     ],
     "prompt_number": 106
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Hm. This is not what we expected. For humans, the x-axis is not understandable. What is $0.0002Hz$? Let's convert it to period, which is the reciprocal of the sampling rate."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Rythm of modern Life, seen in the Power Grid"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Xp = 1.0/X # in seconds\n",
      "Xph= Xp/(60.0*60.0) # in hours"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 107
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(15,6))\n",
      "plt.plot(Xph, 2.0*np.abs(Y[:N])/N)\n",
      "plt.xticks([12, 24, 33, 84, 168])\n",
      "plt.xlim(0, 180)\n",
      "plt.ylim(0, 1500)\n",
      "plt.xlabel('Period ($h$)')\n",
      "plt.savefig('VerticalGridLoadGermany2013-FFT.png',bbox_inches='tight', dpi=150, transparent=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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XzSVDZeeNScrnmfU1ukPOhCVuH2932+Xl5WpoaJAkHTx4UEuWLFFPDNvu/wrS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\nw3u/j7atvO9PV7D6Nef/z9kP9PvaE3j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UaS+L7pNASM0znNG3nO1fH9AITKh8kwL1hxU5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\nW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       "text": [
        "<matplotlib.figure.Figure at 0x110734950>"
       ]
      }
     ],
     "prompt_number": 108
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Aaaaah! Now we see following peaks:\n",
      "\n",
      "* `12h` day/night rythm\n",
      "* `24h` daily rythm\n",
      "* `33.6h` something? Any suggestions?\n",
      "* `84.2h` something? Any suggestions?\n",
      "* `168h` week rythm"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}